A sampling scheme that selects a random 0-1 matrix of size N×M uniformly in the set of 0-1 matrices with predetermined row and column totals is investigated. The limits, as M goes to ∞ and N is fixed, of the column relative frequencies is derived. The limiting values give a sampling design for a population of N units that generalizes the conditional Poisson sampling design introduced by Hajek. A method

The aim of the paper is to demonstrate that the continuous-time frog model can spread arbitrary fast. The set of sites visited by an active particle can become infinite in a finite time.

We consider large neural networks in cognitive neuropsychology whose synaptic connectivity matrices are randomly chosen from correlated Gaussian random matrices. We focus on the moments of characteristic polynomials and prove that the limiting even and odd moments at the edge are given by the largest eigenvalue distribution in the Gaussian Symplectic Ensemble (GSE) and in the induced GSE ensemble,

Two counterexamples, addressing questions raised in Adamczak (2019) and Poly and Zheng (2019), are provided. Both counterexamples are related to chaoses. Let Fn=Yn+Zn, where the random variables Yn and Zn belong to different chaoses of uniformly bounded degree. It may be that Fn⟶a.s0, Fn⟶L2+δ0 and E{supn|Fn|δ}<∞, for some δ>0, and yet Yn fails to converge to 0 a.s.

We introduce the concept of pseudo-independence under sublinear expectations and derive the weak and strong laws of large numbers with non-additive probabilities generated by sublinear expectations.

Classical harmonic oscillators are ubiquitous mechanical systems, appearing in many setups, in particular, as Gauss-Markov processes. The connection between wave motion and harmonic oscillators leads us to a connection between waves and a special class of infinitely dimensional Gauss-Markov processes. It is the aim of this work to explore this connection in the simplest case, namely, that of a linear

In this article, we show that the Brownian motion on the circle constructed by Lévy (1959) is a regular Euclidean Brownian motion on the half-circle with its own mirror image on the other half-circle, and is degenerated in the sense of Minlos (1959). This raises the question of what the white noise is on the circle. We then formally define the white noise space and its associated Brownian bridge on

Sparse Bayesian learning models are typically used for prediction in datasets with significantly greater number of covariates than observations. Such models often take a reproducing kernel Hilbert space (RKHS) approach to carry out the task of prediction and can be implemented using either proper or improper priors. In this article we show that a few sparse Bayesian learning models in the literature

This article presents a quasi-random ranked set sampling approach based on the Halton sequence for natural resource surveys. A design-based variance estimator for the sample mean is also presented.

For real a>0, let Xa denote a random variable with the gamma distribution with parameters a and 1. Then P(Xa−a>c) is increasing in a for each real c⩾0; non-increasing in a for each real c⩽−1∕3; and non-monotonic in a for each c∈(−1∕3,0). This extends and/or refines certain previously established results.

In this paper, we study the following backward stochastic differential equations driven by G-Brownian motion (G-BSDEs in short) Yt=ξ+∫tTf(s,Ys,Zs)ds+∫tTg(s,Ys,Zs)d〈B〉s−∫tTZsdBs−(KT−Kt)with a kind of non-Lipschitz coefficients. An existence and uniqueness theorem is established.

This paper studies the first passage times of a (reflected) Brownian motion with broken drift over a random boundary. The time-dependent Meyer-Tanaka formula allows us to obtain the formulas on the joint Laplace transform of the hitting time and hitting position. This paper extends the results of first rendezvous times of (reflected) Brownian motion and compound Poisson-type processes in Perry et al

A fast and flexible kNN procedure is developed for dealing with a semiparametric functional regression model involving both partial-linear and single-index components. Rates of uniform consistency are presented. Simulated experiments highlight the advantages of the kNN procedure. A real data analysis is also shown.

Let ηn,n≥1, be a sequence of random variables. We study conditions under which limε↘0∑n≥1ϕ(n)P(ηn≥f(εg(n)))−ν(ε)=C,where C is a constant, assuming among other conditions that non-negative functions ϕ(x) and f(x),g(x), tend, respectively, to 0 and to ∞ as x→∞. Results obtained, in particular, are wide generalization of the similar results obtained recently in Gut and Steinebach (2013), Kong (2016),

This note extends the applicability of the Wilcoxon signed rank test to data from asymmetric densities. The operational characteristics and asymptotic properties of the process are discussed in detail. Additionally, a real data example highlights the benefits gained in practice.

Consider the random graph G(n,p) obtained by allowing each edge in the complete graph on n vertices to be present with probability p independent of the other edges. In this paper, we study the minimum number of edge edit operations needed to convert G(n,p) into an Eulerian graph. We obtain deviation estimates for three types Eulerian edit numbers based on whether we perform only edge additions or only

Consider the probability that a binomial random variable Bi(n,m∕n) with integer expectation m is at most its expectation. Chvátal conjectured that for any given n, this probability is smallest when m is the integer closest to 2n∕3. We show that this holds when n is large.

We consider a Gaussian graphical model associated with an equicorrelational and one-dimensional conditional independence graph. We show that pairwise correlation decays exponentially as a function of distance. We also provide a limit when the number of variables tend to infinity and quantify the difference between the finite and infinite cases.

We introduce an estimation method for the scaled skewness coefficient of the sample mean of short and long memory linear processes. This method can be extended to estimate higher moments such as Kurtosis coefficient of the sample mean. Also a general result on computing all asymptotic moments of partial sums is obtained, allowing in particular a much easier derivation of some existing central limit

In this short note, recent results on the predictive power of kernel principal component in a regression setting are extended in two ways: (1) in the model-free setting, we relax a conditional independence model assumption to obtain a stronger result; and (2) the model-free setting is also extended in the infinite-dimensional setting.

The power of the frequency domain causality test proposed by Breitung and Candelon (2006) is analyzed. We show that the power of the test is closely related to the root of the VAR model. When the root of the VAR model is near 1 or −1, the test may have a maximal power at the frequencies close to 0 or π.

An identification result for nonparametrically transformed location scale models is proven. The result is constructive in the sense that it provides an explicit expression of the transformation function.

This paper proposes a nonparametric test of the increasing log-odds rate null hypothesis. A table of simulated p-values is provided and the performance of the test is validated through a simulation study.

Rapidly decreasing tempered stable (RDTS) distributions are useful models for financial applications. However, there has been no exact method for simulation available in the literature. We remedy this by introducing an exact simulation method in the finite variation case. Our methodology works for the wider class of p-RDTS distributions.

We establish various properties of Gaussian processes centered at their online average and discuss their application to goodness-of-fit testing.

We prove that some results claimed for the dispersive ordering are not valid and provide some contributions in this direction. Then, we revisit the dispersive ordering of order statistics from IRHR distributions. Several extensions to generalized order statistics are obtained.

Every element θ=(θ1,…,θn) of the probability n-simplex induces a probability distribution Pθ of a random variable X that can assume only a finite number of real values x1<⋯

It may be thought that the topic of the title of this paper would have been exhausted by now but apparently not. In this note, we lay out both existing and unfamiliar simple functions of independent beta-distributed random variables that themselves follow beta distributions, and explore a number of extensions, generalizations and examples thereof.

Robust concentration inequalities of Bernstein type for sub-exponential random variables are proved with respect to probability measures whose densities are connected by open exponential arcs.

We introduce a family of weighted omega-square statistics. We show that they provide a family of locally asymptotically optimal goodness-of-fit tests, in the sense of Bahadur, for the location problem associated with (type iv) generalized logistic distributions. Our paper extends and unifies some results already known for the classical Cramér–von Mises and Anderson–Darling statistics which are optimal

In this paper we consider the sum Snξ≔ξ1+…+ξn of (possibly dependent and nonidentically distributed) real-valued random variables ξ1,…,ξn with dominatedly varying distributions. Assuming that the ξk’s follow the dependence structure, similar to the asymptotic independence, we obtain the asymptotic lower and upper bounds for the tail moment E((Snξ)m1{Snξ>x}), where m is a nonnegative integer, improving

We study the asymptotic behaviour of a properly normalized time changed Wiener processes. The time change reflects the fact that we consider the Laplace operator (which generates a Wiener process) multiplied by a possibly degenerate state-space dependent intensity λ(x). Applying a functional limit theorem for the superposition of stochastic processes, we prove functional limit theorems for the normalized

In this paper, we study the estimation of integrated covariance matrix based on noisy high-frequency data with multiple transactions using random matrix theory. We further prove that the proposed estimator is also asymptotically optimal for portfolio selection.

In this work, we consider the information generating function measure and develop some new results associated with it. We specifically propose two new divergence measures and show that some of the well-known information divergences such as Jensen–Shannon, Jensen-extropy and Jensen–Taneja divergence measures are all special cases of it. Finally, we also discuss the information generating function for

Different aspects of mean inactivity time (MIT) function such as properties, bounds and limiting behaviour are studied. We proceed to prove an important characterization theorem and also explore weak convergence issues. Finally, connections between MIT and reversed hazard rate functions are examined.

We consider a sequence of correlated Bernoulli variables whose probability of success of the current trial depends conditionally on the previous trials as a linear function of the sample mean. We extend the results of Zhang and Zhang (2015) by establishing an almost sure invariance principle and a weak invariance principle in a larger setting. Moreover, we also state a Gaussian fluctuation related

In this note we consider the optimal design problem for estimating the slope of a polynomial regression with no intercept at a given point, say z. In contrast to previous work, we investigate the model on the non-symmetric interval.

We consider the issue of strong consistency for model selection in a large class of causal time series models, including AR(∞), ARCH(∞), TARCH(∞), ARMA-GARCH and many other classical processes. We propose a penalized criterion based on the quasi likelihood of the model. We provide sufficient conditions that ensure the strong consistency of the proposed procedure. Also, the estimator of the parameter

Inspired by the Edgeworth–Portnoy model for Gaussian time series, a family of randomized moving window (RMW) and randomized moving sum (RMS) models for stationary count time series is proposed. For the RMW process, we derive Markov properties which, in turn, allow to conclude on a connection of the RMS model to the Hidden-Markov model. This connection is used to develop an efficient scheme for maximum

We prove a strong invariance principle for the Kantorovich distance between the empirical distribution and the marginal distribution of stationary α-mixing sequences.

Let B={Bt:t≥0} be a real-valued fractional Brownian motion of index H∈(0,1). We prove that the macroscopic Hausdorff dimension of the level sets Lx=t∈R+:Bt=x is, with probability one, equal to 1−H for all x∈R.

We study the independence assumption in the mixed randomized response model to show that it is unnecessary for unbiasedness and yet preferable for efficiency. The unconditional variance of MRR estimators without the independence condition is shown.

In this paper, a model average approach is developed for linear models with response missing at random by establishing a cross-validation-based weight choice criterion. Its asymptotical optimality is proved and its finite-sample performance is investigated by simulations.

Let {Xn;n≥1} be a sequence of independent and identically distributed random variables in a sub-linear expectation space (Ω,ℋ,E) with a capacity V generated by E. The convergence rate of ∑n=1∞V(|∑k=1nXk|>ϵn) as ϵ→0 is studied. Hedey (1975)’s theorem is shown under the sub-linear expectation.

The common classical approach for finding optimal design is minimizing the variance of an unbiased maximum likelihood estimator (MLE) of parameters. However, under regularity condition, the variance of MLE is approximated by the Cramer–Rao lower bound. In this article, optimal designs are obtained under non-regularity condition in non-linear models. In the Bayesian approach, conditional mutual information

In this paper, we give a two sided estimate on the spectral gap for the Boltzmann measures μn,h with h∈R and n≥3 by reducing multi-dimensional case to one dimensional diffusion. Moreover, the result for the one dimensional diffusion is sharp.

Recent findings for optimal transport maps between distribution functions sharing the same copula show that componentwise the solution is the optimal map between the marginal distributions. This is an important discovery since in the multivariate setting optimal maps are difficult to find and only known in a few special cases. In this paper, we extend the result on common copulas by showing that orthonormal

In the theory of large deviations Schilder’s Theorem is one of the main results. In this paper, we investigate analogous problem for a family {μϵ,ϵ>0} of probability measures associated to a family of positive distributions Φϵ on the dual of some real nuclear Fréchett spaces, followed by some interesting examples.

This paper presents an iterative formulation to compute the central moments of the matrix Fisher distribution on the three dimensional special orthogonal group up to an arbitrary order.

This study proposes original symmetry models with a structure wherein the local odds ratios increase exponentially as the row number of the square contingency table increases in each sub-table. The proposed models provide a better fit than the existing models.

Consider a convex hull generated by a homogeneous Poisson point process in a cone in the plane. In the present paper the central limit theorem is proved for the joint probability distribution of the number of vertices and the area of a convex hull in a cone bounded by the disk of radius T (the center of the disk is at the cone vertex), for T→∞. From the results of the present paper the previously known

We consider an RCAR(p) process and we establish that the standard estimation lacks consistency as soon as there exists a nonzero serial correlation in the coefficients. We give the correct asymptotic behavior and some simulations come to illustrate the results.

In this paper, under the assumption of Hölder continuous coefficients, we prove the strong Feller property for the solution to one-dimensional Lévy processes driven stochastic differential equations. Our proof is based on the tools of Yamada–Watanabe approximation technique, Girsanov’s theorem and coupling method. Using this approach, the continuous dependence on initial data for the same equations

Using Kendall’s tau for copulas, we compare the degree of concordance of random variables with that of their order statistics. We prove a general inequality and show that this inequality is strict for every copula from the Fréchet family which is distinct from the upper Fréchet–Hoeffding bound.

The stationary bootstrap method is popularly used to compute the standard errors or confidence regions of estimators, generated from time processes exhibiting weakly dependent stationarity. Most previous stationary bootstrap methods have focused on studying large-sample properties of stationary bootstrap inference about a sample mean under short-range dependence. For long-range dependence, recent studies

The taboo rate is first defined, which satisfies with the Chapman–Kolmogorov equation. Then the differentials of hitting time distribution are expressed by many different taboo rates, which deeply reveal the intrinsic relationship between the transition rate matrix and the hitting time distribution in continuous-time reversible Markov chains. As an example, the explicit expressions of the differentials

The Haezendonck–Goovaerts (HG) risk measure has received increasing attention in recent years. In this paper, we propose a conditional version of the HG risk measure, called CoHG risk measure. This conditional risk measure can be used to describe a causality relationship between two risk variables and to qualify the systemic risk contribution of a risk in a catastrophic scenario. We list some basic

Various equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically

We propose a double selection instrumental variable estimator for the endogenous treatment effects using both high-dimensional control variables and instrumental variables. It deals with the endogeneity of the treatment variable and reduces omitted variable bias due to imperfect model selection.

For linear mixed models having two variance components, one can compute exact confidence intervals for a ratio of the variances. We show that there is a family of unbiased intervals and highlight those unbiased intervals which have short expected length.